an affine plane is a two-dimensional affine space. There are two ways to formally define affine planes, which are equivalent for affine planes over...

In geometry, an affine plane is a system of points and lines that satisfy the following axioms: Any two distinct points lie on a unique line. Given any...

preserving both the dimension of any affine subspaces (meaning that it sends points to points, lines to lines, planes to planes, and so on) and the ratios of...

wherever their x-coordinate is positive. The Moulton plane has parallel classes of lines and is an affine plane. It can be projectivized, as in the previous example...

producing the topological plane, which is homeomorphic to an open disk. Viewing the plane as an affine space produces the affine plane, which lacks a notion...

two-dimensional plane can be drawn; and, in general, through k + 1 points in general position, a k-dimensional flat or affine subspace can be drawn. Affine space...

axiomatic treatment of plane affine geometry can be built from the axioms of ordered geometry by the addition of two additional axioms: (Affine axiom of parallelism)...

projective and affine spaces because of their regularity and simplicity. Other significant types of finite geometry are finite Möbius or inversive planes and Laguerre...

projective plane. However, its statement in the affine plane is in a sense less informative and more complicated than that in the projective plane. Consider...

always given by affine transformations from one tangent plane to another. This notion of parallel transport of tangent vectors, by affine transformations...